Question

How many molecules of aspirin are contained in a \[100.0{\text{ }}g\] tablet of aspirin \[{C_9}{H_8}{O_4}\]?

Answer 1

Hint:Use the molar mass of aspirin to define how many moles you have in that sample
Use Avogadro's number to change the number of moles to number of molecules

Complete step by step answer:Aspirin has a molecular formula \[{C_9}{H_8}{O_4}\].
 It has a molar mass =\[12{\text{ }}x{\text{ }}9{\text{ }} + {\text{ }}1{\text{ }}x{\text{ }}8{\text{ }} + {\text{ }}16{\text{ }}x{\text{ }}8{\text{ }}g{\text{ }}mo{l^{ - {\mathbf{1}}}}\;\]i.e; \[180.157{\text{ }}g{\text{ }}mo{l^{ - 1}}.\]
 This revenues that one mole of aspirin will have a mass of \[180.157{\text{ }}g.\]
You're distributing with a\[100.0 - g\;\] sample of aspirin, which will be equivalent to
 \[100.0g*{\text{ }}(1{\text{ }}mole{\text{ }}aspirin{\text{ }}/{\text{ }}180.157g){\text{ }} = {\text{ }}0.55507\]moles aspirin
Now that, you identify how many moles of aspirin you have in your sample, use the detail that one mole of a substance holds \[6.022*{10^{23}}\;\] molecules of that substance.
 - this is known as Avogadro's number.

\[\]\[1\]mole = \[6.022*{10^{23}}\;\] molecules = Avogadro's number
Use Avogadro's number as a alteration factor to calculate how many molecules you become in \[0.55507\;\]moles of aspirin
\[0.55507moles*{\text{ }}(6.022*{10^{23}}molecules{\text{ }}/{\text{ }}1mole){\text{ }} = {\text{ }}3.343*{10^{23}}molecules\]
The answer is plump to three sig figs, the number of sig figs you have for the mass of aspirin.

Note:
We regularly find that chemists are involved in determining the number of particles or moles existing in a given mass of sample. To do so, we apply the molar mass of the chemical species involved. The molar mass of a compound or molecule is the mass in grams of one mole of the held chemical species. It is intended by taking the sum of the atomic masses of each element that seems in its molecular formula. For ionic compounds, the molar mass is also recognized as the formula weight.